Question * Determine the nature of convergence of the following improper integrals 00 1 dx 1+ x* A = X 2 dx and B = 1 A converges and B diverges O none of them A diverges and B converges A and B converge

Q: Find the area of the region(s) enclosed by the curv

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5, x=4, and…

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Q: Use any method to simplify the complex fractloh. k+1 25k 3k - 1 15k

A: Use the fraction rule; abcd=a·db·c   The given expression is: k+125k3k-115k

Q: (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D %3D…

A: As you mentioned part b is solved

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t+o 5t2 + 6't (?,?) - (

A: We have to find limit of given function

Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: [7 -3] A = 4 6 B…

A: We know that for a matrix A=abcd=ad-bcA=7-346=7*6-(-3*4)                       =42+12…

Q: Question 11 /4-x² c 3-x²-y² STS xdz dy dx Evaluate the iterated integral. J. J. -5+x²+y? 0, A)…

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Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: 2 1 Evaluate the iterated integral. J J. J. (x² + y2 + z?) dx dy dz -1°0 A) 5 B 3 8 D) 10

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Q: given point. Function Point f(x, y, z) = V x2 + y2 + z² (10, 3, 9) %3D Vf(10, 3, 9) = Find the…

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Q: 'ind the area of the region that is enclosed by the cardiod = 20 + 20 sin 0. OTE: Enter the exact…

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Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Solving

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Consider a field with V = 8a²y² î + 4y²j + –5y² z³k a) Find the divergence of V: V•V: b) Find the…

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: Evaluate the line integral-ydx + xdy along the curve C: y? = 21x from (21, 21) to (0,0). NOTE: Enter…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (ï, §) = (?, ?) y = r

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Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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Q: h sin 2 xdx X COs 2

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: Determine the volume of the solid obtained by roteting the region bounded by y=x^2-2 and y=x about…

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Q: Find the area of the region(s) enclosed by the curve (x) the x-axis, and the lines x = -1 and X= 2.…

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Q: Consider the following functions. f(x) g(x) 8 sin x %3D = 8 cos 2x -

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Directional derivative: D f = del f • unit vector of direction

Q: ne area Of Lhe region

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: The point (– 1, 3) is on the terminal side of 0 in standard position. The exact value of cos(0)is…

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Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Find the area of the shaded region. r = Vcos 20 r = 9 cos 0 NOTE: Enter the exact answer. A =

A: We have to find area of shaded Region.

Q: aluate the iterated integral. || 5x²sin(y) dy dz dx =

A: Given: ∫0π∫05x∫0xz5x2sinydydzdx

Q: Evaluate the double integral over the rectangular region R. / 8xy°dA; R = {(x, y): – 1 < x < 1, – 7…

A: Given:       ∬R8xy6dA   R=x,y: -1≤x≤1 , -7≤y≤7        ∬Rfx,ydA=∫ab∫cdfx,ydydx…

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given

Q: Find the length of the curve, L. y? = 64 (r+ 5)* , 0 0

A: To evaluate the length of the given curve.

Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: Jse a double integral to find the volume under the plane z = 38x + yand over the rectangle R = {(x,…

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Q: 10. y = 1 11. x' +xsin y = ye" 12. In(x+ y) = tan (xy) sin

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Q: Evaluate the double integral over the rectangular region R. y'dA; R = {(x, y): -1sxs1, - 8 <ys 8} |…

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration

Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 19, (1,…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (ë, g) = | (?,?) y = z

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Q: Evaluate JJ Xy dA, where R is the region in LA ... y = x? R 2 A) 13/7 B) 16/3 c) 18 D) 20

A: A detailed solution is given below

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…